back dicate use. everything you write dow silouu B such Remember, Recall Table X
ID: 3173648 • Letter: B
Question
back dicate use. everything you write dow silouu B such Remember, Recall Table XII (text) to find the following probabilities, related to a particular binomial distribution. each that "X" denotes the number of 'successes' out of n trials; 'p' is the probability of "success' on a tri A. If n 12 and p 075, find: POX 10) POX S 8) B. If n 20 and p 075, find: POX 217) i) POX S 13) II. Use Table ll in the text to find the area under the standard normal curve described as follows. A. to the left of z 1.15 B. to the right of z 0.86 C. the right of z 1.10 D. between z 0.55 and z 1.55 E. outside the interval -1.38Explanation / Answer
I. A) n = 12, p = 0.75
i) P(X > 10)
= P(X = 10) + P(X = 11) + P(X = 12)
= 0.232 + 0.127 + 0.032 (From table)
= 0.391
ii) P(X < 8)
= 1 - P(X > 8)
= 1 - [P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)]
=1 - [0.258 + 0.232 + 0.127 + 0.032] (From table)
= 0.351
B) n = 20, p = 0.75
i) P(X > 17)
= P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)
= 0.134 + 0.067 + 0.021 + 0.003
= 0.225
ii) P(X < 13)
= 1 - P(X > 13)
= 1 - [P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)]
= 1 - (0.169 + 0.202 + 0.190 + 0.134 + 0.067 + 0.021 + 0.003)
= 0.214
II. From z table,
A) P(z < -1.15) = 0.1251
B) P(z > 0.86) = P(z < - 0.86) (By Symmetry)
So,
P(z > 0.86) = 0.1949
C) P(z > -1.10) = P(z < 1.10) (By Symmetry)
So,
P(z > -1.10) = 0.8643
D) P(0.55 < z < 1.55)
= P(z < 1.55) - P(z < 0.55)
= 0.9394 - 0.7088
= 0.2306
E) P(Outside the interval -1.38 < z < 1.38)
= 1 - P(-1.38 < z < 1.38)
= 1 - [P(z < 1.38) - P(z < - 1.38)]
= 1 - [0.9162 - 0.0838]
= 0.1676
III. a) We need to find k such that
P(-k < z < k) = 0.82
P(z < k) - P(z < -k) = 0.82
By using symmetry,
P(z < k) = P(z > -k) = 1 - P(z < -k)
So,
1 - 2*P(z < -k) = 0.82
2*P(z < -k) = 1 - 0.82
P(z < -k) = 0.09
From table,
P(z < -1.34) = 0.09
So,
k = 1.34
P(-1.34 < z < 1.34) = 0.82
b) We need to find k such that
P(-k < z < k) = 0.93
P(z < k) - P(z < -k) = 0.93
By using symmetry,
P(z < k) = P(z > -k) = 1 - P(z < -k)
So,
1 - 2*P(z < -k) = 0.93
2*P(z < -k) = 1 - 0.93
P(z < -k) = 0.035
From table,
P(z < -1.81) = 0.09
So,
k = 1.81
P(-1.81 < z < 1.81) = 0.93
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